def grmagnus2(alpha, beta, betad, kp):
# grmagnus with sparse matrices
# From J. Phys. F Vol 14, 1984, 1205, M P Lopez Sancho, J. Rubio
# 20-50 % faster than gravik
# From Huckel IV Simulator
global I
tmp = linalg.inv(alpha.todense()) # Inverse part of Eq. 8
t = (-1*tmp)*(betad).todense() # Eq. 8 (t0)
tt = (-1*tmp)*(beta).todense() # Eq. 8 (t0 tilde)
T = t.copy() # First term in Eq. 16
Toldt = I.copy() # Product of tilde t in subsequent terms in Eq. 16
change = 1 # Convergence measure
counter = 0 # Just to make sure no infinite loop
etag = 0.000001
etan = 0.0000000000001
while linalg.norm(change) > etag and counter < 100:
counter += 1
Toldt = Toldt*tt # Product of tilde t in subsequent terms in Eq. 16
tmp = I - t*tt - tt*t
if (1/(linalg.cond(tmp))) < etan:
g = 0
print "1: tmp NaN or Inf occured, return forced. Kp: " + str(kp)
return g
tmp = faster_inverse(tmp) # Inverse part of Eq. 12
t = (tmp*t*t) # Eq. 12 (t_i)
tt = (tmp*tt*tt) # Eq. 12 (t_i tilde)
change = Toldt*t # Next term of Eq. 16
T = T + change # Add it to T, Eq. 16
if isnan(change).sum() or isinf(change).sum():
g = 0
print "2: tmp NaN or Inf occured, return forced. Kp: " + str(kp)
return g
g = (alpha + beta*T)
if (1/(linalg.cond(g))) < etan:
g = 0
print "3: tmp NaN or Inf occured, return forced. Kp: " + str(kp)
return g
g = faster_inverse(g)
gn = (abs(g - linalg.inv(alpha - beta*g*betad)))
if gn.max() > 0.001 or counter > 99:
g = 0
print "4: Attention! not correct sgf. Kp: " + str(kp)
return g
# Help save memory
del tmp, t, tt, T, Toldt, change, counter, etag, etan, gn
return g
def grmagnus(alpha, beta, betad, kp):
# From J. Phys. F Vol 14, 1984, 1205, M P Lopez Sancho, J. Rubio
# 20-50 % faster than gravik
# From Huckel IV Simulator
tmp = linalg.inv(alpha) # Inverse part of Eq. 8
t = (-1*tmp)*(betad) # Eq. 8 (t0)
tt = (-1*tmp)*(beta) # Eq. 8 (t0 tilde)
T = t.copy() # First term in Eq. 16
Id = eye(alpha.shape[0]) # Save the identity matrix
Toldt = Id.copy() # Product of tilde t in subsequent terms in Eq. 16
change = 1 # Convergence measure
counter = 0 # Just to make sure no infinite loop
etag = 0.000001
etan = 0.0000000000001
while linalg.norm(change) > etag and counter < 100:
counter += 1
Toldt = Toldt.dot(tt) # Product of tilde t in subsequent terms in Eq. 16
if (1/(linalg.cond(Id - dot(t,tt) - dot(tt,t)))) < etan:
g = 0
print "1: tmp NaN or Inf occured, return forced. Kp: " + str(kp)
return g
tmp = linalg.inv(Id - t.dot(tt) - tt.dot(t)) # Inverse part of Eq. 12
t = tmp.dot(t).dot(t) # Eq. 12 (t_i)
tt = tmp.dot(tt).dot(tt) # Eq. 12 (t_i tilde)
change = Toldt.dot(t) # Next term of Eq. 16
T = T + change # Add it to T, Eq. 16
if isnan(change).sum() or isinf(change).sum():
g = 0
print "2: tmp NaN or Inf occured, return forced. Kp: " + str(kp)
return g
if (1/(linalg.cond(alpha + beta.dot(T)))) < etan:
g = 0
print "3: tmp NaN or Inf occured, return forced. Kp: " + str(kp)
return g
g = linalg.inv(alpha + beta.dot(T))
gn = abs(g - linalg.inv(alpha - beta.dot(g).dot(betad)))
if gn.max() > 0.001 or counter > 99:
g = 0
print "4: Attention! not correct sgf. Kp: " + str(kp)
return g
nan_inf_flag = 0
# Help save memory
del tmp, t, tt, T, Id, Toldt, change, counter, etag, etan, gn
return g